The Mental Representation of Universal Quantifiers
Tyler Knowlton, Paul Pietroski, Justin Halberda, Jeffrey Lidz
February 2019

The meaning of sentences like "every circle is blue" could be represented in speakers’ minds in terms of individuals and their properties (e.g., for each thing that’s a circle, it’s blue) or in terms of relations between groups (e.g., the blue things include the circles). Formally, both the tools of first-order logic and the tools of second-order logic can be used to represent the meaning of universally quantified statements. We offer evidence that this formal distinction is psychologically realized in a way that has detectible symptoms. Specifically, we argue that, despite the truth-conditional equivalence of statements with universal quantifiers, "each"- statements are represented in first-order terms but "every"- and "all"-statements are represented in second-order terms. The crucial finding is that participants have a better estimate of a set’s cardinality – a fundamentally group property – after evaluating statements with "every" or "all" than after evaluating statements with "each". Our results support the idea that quantifier meanings are mentally represented at a finer grain size than truth-conditions.
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Reference: lingbuzz/004486
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keywords: natural language quantifiers, meaning, logic, experimental semantics, semantics
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